A mold to make a plastics material piece includes two parts defining a cavity corresponding to the piece to be made, each part has a peripheral zone for coming into contact with the other part's peripheral zone to define the mold's joint face. One part is made up of two blocks, namely a central block and a peripheral block, the two blocks suitable for sliding relative to each other in the mold closure direction, and the peripheral block capable of movement so as to move the peripheral zone away from the edges of the sheet. A method of making a plastics material piece includes placing a sheet in a part of a mold, moving a peripheral block, closing the mold, and moving the peripheral block to a molding position while keeping the first and second peripheral zones in contact.
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